Hybrid inertial/magnetic system for determining the position and orientation of a mobile body

ABSTRACT

The present invention concerns a system for contactless determination of the position and orientation of a first mobile object (M) relative to a reference mark (R P ) carried by a second fixed or mobile object (P), in a disturbed electromagnetic environment comprising a transmitting antenna (E) with ferromagnetic cores (E- 1 ) having magnetic permeability higher than 10, incorporating sensors (E- 3 ) for measuring the magnetic field X u  actually emitted by the axes of the ferromagnetic cores. A means ( 4 - 4 ) for extracting the signal correlated with the ambient noise X BR  (T k -K b T c )—from the sensors (Sb) fixed in the platform (P), forms, with measurement X u  of the emitted magnetic induction, a complete model of the measured fields, making it possible to extract, without errors, the six parameters relative to the field model without disturbances.

FIELD OF THE INVENTION

The field of the invention is the measurement of the position and orientation of a mobile body M, which moves in translation and rotation relative to a reference mark connected to a fixed or mobile structure P relative to an inertial reference frame type fixed reference mark. In particular, the invention concerns the determination of the position and orientation (P/O) of the helmet of a pilot in the reference mark of the aircraft, P/O from which the angular position of an external target is determined in said same mark by sight through a system including the helmet-mounted display of the pilot. In a known manner, the pilot superimposes on the external target the image of a collimated cross projected on the transparent visor thereof, and acquires the measurement taken by the device by pressing on a push-button.

More specifically, concerning the devices for determining the P/O called trackers of magnetic technology, the main problem of determining the position and orientation of a mobile body relative to a reference mark connected to a fixed or mobile structure having to be accurately determined comes from an electromagnetic environment significantly disturbed by radiated magnetic fields (EMI for Electromagnetic Interferences, ECI for Eddy Current Interferences or fields due to Eddy currents) and/or magnetic fields induced by ferromagnetic bodies (FMI for FerroMagnetic Interferences), environments such as the cockpits of aircraft and more specifically of helicopters, surgical operating rooms, etc. Thus, the accuracy is significantly degraded in the presence of said interferences. Therefore, the problem consists of finding the means to improve the performances despite the disturbances.

PRIOR ART

U.S. Pat. No. 7,640,106 is known in prior art describing an apparatus for determining the position of a selected object relative to a moving reference image, the apparatus including at least one reference frame transceiver assembly secured to the moving reference frame, at least one object transceiver assembly firmly attached to the selected object, an inertial measurement unit firmly attached to the selected object, an inertial navigation system secured to the moving reference image, and a tracking processor coupled with the object transceiver assembly, to the inertial measurement unit and to the inertial navigation system, the object transceiver assembly communicating with the reference frame transceiver assembly using magnetic fields, the inertial measurement unit producing IMU inertial measurements of motion of the selected object relative to an inertially fixed reference frame, the inertial navigation system producing INS inertial measurements of motion of the moving reference frame relative to the inertially fixed reference frame, the tracking processor receiving electromagnetic measurements resulting from the magnetic communication between the reference frame transceiver assembly and the object transceiver assembly, the tracking processor determining the position of the selected object relative to the moving reference frame by using the IMU inertial measurements and the INS inertial measurements to optimise the electromagnetic measurements.

Patent FR2807831 is also known in prior art describing a device for measuring the position and orientation of a mobile object relative to a fixed structure, in a disturbed magnetic environment, including:

-   -   a first assembly of orthogonal coils emitting magnetic fields,         secured to the fixed structure, defining a reference mark;     -   a second assembly of orthogonal coils receiving magnetic         field(s), secured to the object, and forming a sensor, each of         the coils belonging to a sensor channel.

Such a device includes means:

-   -   for simultaneous and continuous field emission, on the coils of         the first assembly;     -   for measuring, on the sensor channels, the vector sum of the         emitted fields and of the disturbance fields generated by the         environment;     -   for evaluating the disturbance fields;     -   for estimating fields emitted in an undisturbed environment, by         suppressing the evaluated disturbance fields from the vector         sum;     -   for computing the position and orientation of the object in the         reference mark.

U.S. Pat. No. 5,646,525 describes another example of equipment for determining the position and orientation of a helmet worn by a crew member in a vehicle including a generator, associated with the vehicle, which produces a rotating magnetic and electric field of fixed strength, the orientation and frequency within at least a portion of the vehicle. The apparatus also includes a plurality of detectors each of which generates a signal proportional to at least one of the electric or magnetic fields at least one point associated with the helmet and calculation circuitry responsive to the signal for determining the coordinates of the at least one point relative to the generator and for determining the position and orientation of the helmet.

U.S. Pat. No. 6,400,139 also describes an example of apparatus for position/orientation tracking within a bounded volume. Said methods and said apparatus employ at least one fixed sensor, called a “witness sensor,” having a fixed position and orientation near or within the volume to account for electromagnetic distortion. One or more probe sensors are placed on an object having to be tracked within the volume, and the output of each witness sensor is used to compute the parameters of a non-real effective electromagnetic source. The parameters of the effective source are used as inputs for the computation of the position and orientation measured by each probe sensor, as if the object were in the non-distorted electromagnetic field produced by the effective source or sources. In addition to trackers for the helmet-mounted displays in aircraft, tank, and armoured-vehicle applications, the invention finds utility in any electromagnetic tracking system which might be subject to electromagnetic distortion or interference.

DISADVANTAGES OF PRIOR ART

In general, the solutions of prior art do not teach solutions to compensate the disturbances not correlated with the transmitters (actual emitted fields).

U.S. Pat. No. 7,640,106 requires a first inertial sensor in the helmet and a second inertial sensor and an estimator (Kalman filter) for determining an orientation of an object. Said solution requires providing a sensor on the fixed platform. It aims to know the angular orientation of the helmet in the mark of the platform. Said angular orientation is determined through incorporation of the estimated relative velocity. Said relative velocity is obtained by measuring the difference between:

-   -   the angular velocity of the mobile body measured at the output         of an IMU angular velocity sensor attached to the mobile body,         the orientation of which is to be determined, measured in a         fixed inertial frame (inertial reference frame) and     -   the angular velocity of the inertial platform measured by an INS         type inertial unit.

Said solution therefore requires a double inertial system, doubling the noise and the errors.

Furthermore, said solution does not take into account the strong electromagnetic disturbances observed in a real cell, for example, a helicopter or aeroplane cell.

Furthermore, said solution requires an estimation to be carried out of the angular velocity.

The solution taught by the U.S. Pat. No. 6,400,139 on the interpolation of data coming from a plurality of sensors in view of creating a model of the fields sent by real sources, and modelling unknown or dummy sources to compensate the Eddy current disturbances. Said solution consists of installing a plurality of fixed witness sensors in the vicinity of the volume in which the mobile body moves, in order to construct a model of the field measured by said witness sensors. Said model is used for recomputing by interpolation the field measured by the sensor positioned on the mobile object. Same does not make it possible to compensate the disturbance fields of Eddy currents.

Nor does same make it possible to process the disturbances of radiated and non-correlated disturbances (EMI), but only the ECI type disturbances correlated with the emitted radiative field.

All of the solutions of prior art require the use of an additional inertial platform, to determine an additional mark in addition to the reference system provided by the inertial system of the aircraft; which complicates the implementation and the errors.

SOLUTION PROVIDED BY THE INVENTION

The aim of the invention concerns a system as stated by claim 1, aiming to remedy the disadvantages of prior art and to establish a method and produce a process for eliminating electromagnetic disturbances (ECI: Eddy currents, FMI: induced ferromagnetism) in real time without requiring the very expensive need to map the effective volume scanned by the sensor.

Another aim of the invention is to improve the signal-to-noise S/N ratio of the P/O detector for obtaining the required performances in environments significantly disturbed by EMI (for example, in aircraft and more specifically in helicopters: radiated fields created by on-board generators and on-board equipment). The signal-to-noise S/N ratio may be expressed as the ratio between the standard deviation of the signal Sc received by the sensor in “free space”, i.e. without any electromagnetic disturbance and the standard deviation of the noise B, the noise being the sum of all of the signals not coming directly from the transmitter (inductive field).

The purpose of the invention is to achieve an improvement of the S/N ratio in the order of 1000 for the most critical cases (helicopters).

A third aim of the invention is to compensate the latency of the output information through hybridisation with an inertial system.

By referring to FIGS. 2, 3 and 4 which will subsequently be explained, it is indicated that functions of the invention:

-   -   Deploy an optimised transmitter E in the following directions:         -   Generation of alternating currents by E-2 according to a             specific temporal pattern on a finished temporal support and             being repeated sequentially. Said pattern is preferably a             Pseudo-Random Binary Sequence (PRBS) generated by E-4 of the             processor 4.         -   Multiplication by three to ten of the signal emitted             relative to the transmitters of prior art (comparable             reference distance, volume). The method consists of             optimising the winding shapes of the transmission axes to             increase the number of turns for a given diameter of wire             and to introduce a core of very permeable material of             specific shape for increasing the induction emitted in             ratios higher than 10: E-1.         -   Reduction of the total power, and in particular the power             lost by joule effect which increases the temperature and may             cause the results to shift (expansions, deformations, etc.),             which amounts to reducing the emission current.         -   Control E-2 of the system in magnetic field thanks to             sensors E-3 (also known as “sensors_E”) included in the             coils of the transmission axes.         -   Control of the magnetisation of the magnetic coils by             measurement of the symmetry of the alternating currents             injected by E-1-2.     -   Measure the total field by a sensor with Ne axes C-1 the         bandwidth of which ranges from a few tens to a few thousands of         Hertz the output Sc of which is at Ne components.     -   Acquire by the processor 4 the data Xu from E, Sc A=         ,θ,φ from C-1, Sp from C-2, angular velocity of the object M and         the attitudes of the platform both from C-3, all of the inertial         measurements.     -   Filter the various disturbances (noises) of Sc (measurement of         the sensor_C from C-1), i.e. the radiated disturbances (EMI),         the disturbances created by the Eddy currents (ECI for Eddy         Current Interferences) circulating in the conductors situated in         a close volume and caused by the variable fields emitted by the         transmitter, as well as the FerroMagnetic effects (FMI for         FerroMagnetic Interferences):         -   The noised signal Sc is measured by the receiving assembly             C-1, the noise Sp is measured and estimated from the             measuring device C-2. It will subsequently be described that             in a particular embodiment, according to the conditions of             the environment, the noise may be estimated from the device             C-1 preferably over a time during which no current is sent             into the coils E-1 by E-4.         -   Said filtering, subsequently explained, in a first             embodiment, is performed in the processor 4-4 by             constructing a temporal model of the preceding disturbances             and by estimating therefrom the parameters using an optimal             or sub-optimal filter in real time over short times T_(off)             during which the currents injected into E-1 are zero. The             variables of said model are magnitudes varying over time,             independent or weakly correlated from the statistical point             of view that make it possible to show the variations of             useful signals and noises. In a second embodiment, an             embodiment of the ambient noise S_(b) is measured by a             sensor block C2, a complete model of which is modelled as             previously. The parameters of said model are used to             eliminate by subtraction all of the components of S_(b)             correlated with the fields emitted by E-1. Thus, the             non-correlated noise is extracted to become an independent             variable of the linear magnetic model of the signals             measured by the sensor C-1 attached to M.         -   Determine, from all of the parameters identified, the             parameters of the single model of the fields emitted by the             axes of the transmitter (field known as undisturbed “free             space”) and in particular the matrix for computing in a             known manner the position and orientation of the mobile             object.     -   Improve the dynamic behaviour of the detector, in particular by         minimising the latency of the detector, i.e. the time between         the real instant of occurrence of an event over the magnitude to         be measured and the detection thereof by the P/O determination         system. Said improvement is made through hybridisation of the         preceding magnetic detection with an inertial assembly for         measuring the angular velocities of the mobile object and use of         the attitudes of the inertial unit of the platform.

In the invention which will subsequently be described in more detail, the currents injected into the windings that create the inductions, are preferably simultaneous. The measured inductions are therefore the sum of the fields emitted at instant t and the fields present in the environment. Therefore, the aim of the invention is to distinguish in the measured field each component emitted by each transmission axis. Said recognition of the field emitted by one of the components constitutes demultiplexing of the inductions that can be functionally qualified by comparison with the inventions cited that either perform temporal demultiplexing (emission not simultaneous but sequenced over time) or frequential demultiplexing (detection of frequencies in the spectral range). When the fields are demultiplexed, it is considered that three independent emissions were received on three sensor axes.

As regards the hybrid system, the principle of the invention consists of using the attitude provided by the magnetic tracker means expressed in the fixed inertial frame to reset or initialise the computation of the attitude of the IMU gyrometric sensors obtained by incorporation into the inertial frame of a dynamic equation for predicting a quaternion. The attitude of the tracker means expressed in the inertial frame simply uses the attitude of the platform provided by the INS, in the form of three Euler angles or DCM matrix (direction cosine matrix of the platform) or of the quaternion computed from the Euler angles or DCM matrix. The dynamic prediction model, computed at high speed, is reset to time t−T_(L), T_(L) being the latency time of the magnetic tracker means, at each arrival of the quaternion provided by the magnetic tracker means. The information necessary for computing the quaternion (in particular the angular velocities of the IMU of the mobile object) having been stored in memory over time T_(L), the quaternion prediction model is recomputed from t−T_(L) up to the current time t by using the velocities stored in memory. Beyond t up to the next arrival of the magnetic tracker information, the quaternion is computed at the frequency for acquiring angular velocity measurements. The invention also comprises the real time correction of the triaxial angular velocity sensor by estimation of the errors of the sensor.

DESCRIPTION OF A NON-LIMITING EXAMPLE OF THE INVENTION

The present invention will be better understood upon reading the following description, concerning non-limiting examples of embodiments of the invention referring to the appended drawings where:

FIG. 1 shows a schematic view of a solution of prior art

FIG. 2 shows a schematic view of the mark and object reference system

FIGS. 3 and 3′ shows a schematic view of the architecture of the invention

FIG. 4 shows a schematic view of the detailed architecture of the invention

FIG. 5 shows a schematic view of the control of the emitted inductions

FIG. 6 shows a schematic view of a transmitter block of prior art

FIG. 7 shows the schematic view of the formation of an axis E1 of the transmitter according to the invention

FIG. 8 shows examples of embodiment of transmission axes

FIG. 9 shows a schematic view of a core installer according to the invention

FIG. 10 shows a schematic view of the field control

FIG. 11 shows the temporal transmission diagram

FIG. 12 shows a schematic view of magnetic-inertial hybridisation and inertial extrapolator

GENERAL DESCRIPTION OF THE INVENTION

According to FIG. 2, the system for contactless determination of the position and orientation (P/O) of a first object M the associated orthogonal mark R_(M) of which is mobile relative to a reference mark carried by a second object P (Platform), fixed or mobile relative to an inertial reference frame Ri of fixed orientation relative to the stars situated at the centre of the Earth. Said device is arranged in a disturbed electromagnetic environment. A transmitter E consisting of Ne coils forming a quasi-orthogonal mark R_(E) is rigidly attached to the platform P. The transfer matrix R_(E/P) between transmitter mark R_(E) and platform mark R_(p) is presumed constant and measured during installation of the mechanical reference of the transmitter in the platform P. When the mark R_(p) is mobile relative to Ri, as is the case when the platform is an aircraft, the mark R_(p) is defined in the mark Ri by the Euler angles defining the attitude and computed by the inertial unit or an equivalent device and transmitted to the process of the invention. It should be noted that the quaternion Q_(PI) like the transfer matrix R_(p/I) between R_(p) and R_(i) represent the attitude of P relative to R_(i). On the mobile object M are rigidly attached the magnetic sensor with Nc quasi-orthogonal axes C-1 known as sensor_C and the inertial sensor C-3-1 of three orthogonal axes angular velocities. The latter sensor is for example of MEMS (Micro-Electro-Mechanical Systems) type. Same measures the angular velocities in its own reference mark R_(gi) the orientation of which is presumed known by an in-factory measurement according to procedures known by the person skilled in the art. The sensor C-1 is a sensor for measuring the magnetic induction field of fluxgate, fluxmeter, controlled fluxmeter, Hall effect sensor, AMR, GMR, TMR, etc. The axes thereof are defined by the transfer matrix R_(c/M) fixed and identified in the factory in a known manner. In the case of some applications for which the environments are significantly magnetically disturbed by EMI, a particular embodiment consists of adding a certain number of sensors known as sensor_B represented by block C-2 in FIG. 3. Said sensors are attached to the platform. Said sensors are 1 to 3-axis sensors of the same type as the magnetic sensor C-1, and the number thereof is higher than or equal to 1. The orientation and position thereof may not be known accurately, which constitutes an advantage. Same are placed at a sufficiently large distance from the transmitter in the environment of the platform in order to measure as little as possible the field emitted by the transmitter E. The aim is to measure the EMI present in the environment of the sensor C-1. Ideally, a single axis is sufficient but one or more 1 to 3-axis sensors may have to be placed close to specific equipment of the platform to measure harmful disturbances related to said item(s) of equipment.

General Architecture

FIG. 3′ shows a schematic view of the hardware architecture of the system according to the invention.

The mobile body (M) is a helicopter pilot helmet, the cell of the helicopter forming the platform (P).

On the helmet (M) are attached an electromagnetic sensor (C-1) and an IMU inertial sensor (C-3-1); said two sensors are mechanically connected in a rigid manner to the helmet (M).

On the platform P are attached:

-   -   a transmitter E     -   an inertial platform c-3-2     -   a reference electromagnetic sensor C2.

A computer (4-4) receives the signals from said various components and carries out the processes described below.

FIG. 4 explains the assemblies known as “blocks” and shown in FIGS. 2 and 3:

A first assembly E for transmitting magnetic induction(s), comprising a first transmitting sub-assembly E-1 of Ne, Ne being equal to at least two transmitting coils, the axes of symmetry of which, not parallel with one another, form a mark R_(E) attached to the second object P.

A first receiving assembly C-1, attached to said mobile object M and comprising Nc>=2 non-parallel receiving coils, forming a mark R_(C1), sensitive to the ambient magnetic field resulting from the vector sum of the fields emitted by said first transmitting assembly E and disturbing magnetic fields generated by electric currents existing in the environment and by ferromagnetic magnetisations, said second assembly forming a sensor C-1 secured to the first mobile object M and such that the product Nc*Ne>=6, the first mobile object M has a reference mark R_(M). The orientation of the mark R_(C1) relative to the mark R_(M) is constant and noted by RC1/M the direction cosine matrix of the axes of C-1 in RM.

The Nc components of SC form the output of said first receiving assembly C-1.

A computing processor 4 for computing the position and orientation of the first mobile object, coupled with the first analogue/digital conversion (or ADC) means 4-1 for carrying out the acquisition, at discrete times t_(k)=k*Te, of analogue signals S_(c), X_(u1) and S_(b) according to FIG. 4 which will be described better subsequently, the second analogue/digital conversion means E4 which generate the command of the temporal sequence of currents.

Notations

In a preferred embodiment, Ne=Nc=3 will be taken.

The total field B_(TE), three-component vector (pseudo vector), existing at the centre of the sensor is the sum of the following inductions:

{right arrow over (B)} _(TE) ={right arrow over (B)} _(EU) +{right arrow over (B)} _(EMI) +{right arrow over (B)} _(ECI) +{right arrow over (B)} _(FMI) +{right arrow over (B)} _(Γ)  [1]

with

{right arrow over (B)} _(EU) ={right arrow over (B)} _(EU1) +{right arrow over (B)} _(EU2) +{right arrow over (B)} _(EU3)  [2]

where B _(EUj) is the induction expressed in the transmitter mark, and emitted by the transmission axis j (j=1 to 3) at the centre of the sensor C-1. It is presumed in the equation [2] that the emission is simultaneous on the three transmission axes El, since B_(EU) is the sum of the three inductions.

B_(EMI) is the vector of the induction radiated in the environment, for example generated by the currents circulating in the electrical equipment, by the on-board generators, by the 50-60 Hz sector, etc. Same can be modelled by the sum of periodic fields Bsc not correlated with the B_(EUj) and fields B_(R) which are EMI signals the characteristics of which are presumed random because they cannot be represented by deterministic signals of known or estimated characteristics.

{right arrow over (B)} _(RM)(t _(k))={right arrow over (B)} _(SC) +{right arrow over (B)} _(R)  [3]

B_(ECI) is the induction vector at the centre of the sensor, created by the Eddy currents in the conductors situated in the environment of the P/O system, same produced by the magnetic field emitted by the transmitting antenna at the location where the conductors are found.

B_(FMI) is the induction vector at the centre of the sensor, created by the magnetisation of ferromagnetic materials situated in the environment of the P/O system.

B_(T) is the induction of the earth's magnetic field.

It should be noted that, according to FIG. 4, the induction B_(EU) is the useful signal very strongly correlated with the emitted currents and more specifically B_(EU) is linearly dependent on the measurements Xu of the fields emitted by the three axes El and measured according to E-3, the inductions B_(ECI) and B_(FMI) are also strongly correlated with the emitted field Xu.

One of the aims of the invention is to eliminate by filtering all of the inductions so as to only keep the measured vector the model of which is expressed by B_(CU)=[R_(c/e)]^(t)(B_(Eu1)+B_(Eu2)+B_(Eu3)) where B_(EU1), B_(EU2), B_(EU3) are the three-component vectors of the field emitted and received at the centre of the sensor (expressed in the mark of the transmitter) and R_(C/E) is the rotation of the sensor mark relative to the mark of the transmitter. Demultiplexing of the transmission channels is carried out (recognition of the portion of the signals that comes from the transmission channel j=1 to 3) i.e. to determine the components Bc₁ Bc₂, Bc₃ of the sensor C-1 coming from the emission of the axes 1, 2 and 3 of the transmitter E-1 in order to form the 3×3 matrix: [Bcu]=[Bc₁|Bc₂|Bc₃]. The method for computing the rotation of the sensor is obtained in a known manner (U.S. Pat. No. 4,287,809 Egli): knowing Bcu, an estimation of B_(EU) is deduced by using an induction model in free space (without disturbances): R_(CE)=B_(C)B_(EU) ⁻¹.

From the matrix [R_(c/e)], the Euler angles or the quaternion Q^(EM), which are two representations of the attitude of the object M, are taken in a known manner.

The static and dynamic accuracy performances are obviously increasing with the S/N ratio. The increase of the S/N ratio sought is obtained in two obvious and complementary manners: increase the power (or the amplitude) of the useful signal in particular in low frequency and jointly reduce the power of the noise by filtering.

Transmitting Assembly E

A first aim of the invention is the assembly E which includes according to FIG. 4:

-   -   a second transmitting sub-assembly consisting of Ne means of         injection E-2 of predetermined currents through said j coils         E-1, j=1 to Ne of said first assembly E in order to generate a         predetermined induction flux Fj(t) as a function of the time         according to the characteristics specific to each axis j of said         coils; a preferred embodiment consists of including in the         interior volume of said j coils E-1 a highly permeable magnetic         material of the type ferrite bar or Mu-metal wires or of         ferromagnetic alloy such as Vitrovac, Permalloy, etc. Said         magnetic material as will be subsequently described makes it         possible to multiply the magnetic induction under certain         conditions of form which will be discussed.     -   a third sub-assembly E-3 of said first transmitting assembly E         consisting of means of measurement of the electromotive force         due to the induction flux Fj(t) relative to each axis of said Ne         transmitting coils E-1, said assembly E-3 includes one magnetic         sensor for each transmission axis which measures the flux         emitted and one electronic for adapting the signals E-3-2. Any         magnetic induction sensor (fluxgate, controlled fluxmeter, Hall         effect sensor, AMR, GMR, TMR) may also be suitable for measuring         said fields. However, a preferred embodiment consists of winding         the turns concentrically relative to the coils E-1 to form a         simple fluxmeter sensor. A voltage amplifier E-3-2, preferably         comprising a pure incorporation of the signals such that the         magnitudes X_(Uj) are homogeneous to a magnetic induction,         produces the interface on one hand with the ADC acquisition         system 4-1 of the processor 4, on the other hand with the block         E-2 which constitutes the current control device of the coils         E-1. The input or setpoint of the control E-2 is the         three-component signal V_(IC) provided by the block E-4 which is         the generator of the sequence of Ne predetermined cyclical         currents of periodicity Tobs. Said block may be autonomous         (memory equipped with a sequencer and containing the sequences         of setpoint values of the currents) or even, in a preferred         embodiment indicated in FIG. 4, incorporated into the processor         4. The values of the sequence are preferably random binary         values, the sequence is known as PRBS for Pseudo-Random Binary         Sequence, the embodiment and properties of which are known by         the person skilled in the art. The binary values of the sequence         between −V_(IC) and +V_(IC) volts are provided with the         recurrence of T_(e)=T_(obs)/N_(obs) where N_(obs) is the         characteristic number of values of the sequence generated. Same         are deterministic signals over the duration T_(obs) of constant         spectral density as a random noise known as white, over the         range of frequencies between 1/T_(obs) and 1/T_(e). FIG. 5 shows         for one of the axes j the transfer functions of blocks E-1, E-2,         E-3 from FIG. 4 which form part of the control of the emitted         magnetic induction. The signals Xu_(j) constituting the         measurement of the magnetic inductions emitted by the axes E-1         are subtracted from the corresponding signals V_(IC) to form the         error ε of the control, same is processed by a corrector network         E-2-1 which compensates in a known manner the transfer function         of the current amplifier and mainly the time constant T of the         windings with magnetically permeable core E-1, the time constant         T being close to the ratio between the total inductance L and         the resistance r_(b) of the coil. The transfer function of the         current generator block E-2-2 takes into account said         characteristics of the winding. The magnetic field Hi produced         by the current is proportional to the number of turns per unit         of length n with a coefficient of proportionality K_(b) which         depends in a known manner on the geometrical shape of the         winding. The magnetisation of the core is based on the sum of Hi         and the disturbing magnetic fields present in the environment         H_(EMI). The magnetic induction B_(E) produced in a point of the         space outside of the windings by the currents and the core may         be written B_(E)=μ_(eff)·(H_(I)+H_(EMI)) where μ_(eff) effective         permeability, represents the proportionality term between the         magnetic excitation field and the output magnetic induction, the         magnetic field H_(I) is proportional to n*I, “n” being the         number of turns per unit of length and I is the intensity of the         current circulating in the turns of the transmitting coil E-1.         It is known that said coefficient μ_(eff) is based on the         relative permeability of the magnetic material, of the         geometrical shape of the cores, said shape determining the         demagnetising field within the material, of the ratio between         the interior volume of the coil and the volume of the material,         but also losses by Eddy currents. The means for obtaining the         values of μ_(eff)>>100 will subsequently be indicated. In said         control, the detector of the electromotive force E-3-1         previously described has a transfer function K_(BV)*p         (derivation with induction conversion variation         ΔB_(E)/Volt=K_(BV) into Tesla per Volt). The block E-3-2 carries         out a pure incorporation of gain K_(CR) to obtain a homogeneous         output with the setpoint Vic.

The main object of said control is to cancel out the EMI magnetic fields present in the environment which are added to the exciter field proportional to n*I_(j), where I_(j) is the current relative to the winding j, but also to linearise the coefficient μ_(eff) because it is known that the magnetisation of magnetic materials has a non-linear magnetisation curve with saturation for the strong excitations.

From FIG. 5, it is easily shown that the output B_(E) is the following:

$B_{E} = {{\frac{G \cdot F}{1 + {G \cdot F}}\frac{V_{ic}}{F}} + {\frac{\mu_{eff}}{G \cdot F}H_{EMI}}}$ with $F = \frac{\Delta \; V_{IC}}{\Delta \; B_{E}}$ and ${G = {K_{G}\frac{K_{A}}{R}{K_{b} \cdot n \cdot \mu_{eff}}\frac{1 + {\hat{T}p}}{1 + {Tp}}}};$

μ_(eff) is the effective permeability if in addition in the useful band: GF>>1

$\begin{matrix} {{B_{E} \approx {\frac{V_{ic}}{F} + {\frac{\mu_{eff}}{\mu_{0} \cdot G \cdot F}B_{EMI}}}} = {\frac{V_{ic}}{F} + {\frac{\mu_{r\_ eff}}{G \cdot F}B_{EMI}}}} & \lbrack 4\rbrack \end{matrix}$

with μ_(r) _(_) _(eff) effective relative permeability

where B_(EC) is the induction produced at the centre of the core and μ_(r) _(_) _(eff) the effective relative permeability. The signal-to-noise ratio in the coreless and control-less configuration is

$\frac{V_{ic}}{F}/{B_{EMI}.}$

With core for E-1 and control E-2, it is seen that the signal-to-noise ratio is

${\frac{V_{ic}}{F}/\frac{\mu_{r\_ eff}}{G \cdot F}}{B_{EMI}.}$

To keep the same signal-to-noise ratio whilst keeping the same order of magnitude for B_(E) in output, it is therefore necessary that G·F≧μ_(r) _(_) _(eff). Said relation defines the minimum gain of the control chain. The corrector network of the shifted proportional type K_(G)(1+Tp) must be adjusted according to the rules known for ensuring the stability of the control. It is also possible to produce a PID according to the techniques taught automatically. Another interesting aspect of the invention is the linearisation of the field emitted by the control. As μ_(r) _(_) _(eff) is a highly non-linear function, the harmonics B_(harmo) appear as output of E-1 in drawing 5. If the output is expressed according to the inputs V_(ic), B_(EMI) and B_(harmo), the following is obtained:

$\begin{matrix} {{B_{E} = {\frac{G \cdot F}{1 + {G \cdot F}}\left( {\frac{V_{ic}}{F} + \frac{B_{harmo}}{G \cdot F} + {\frac{\mu_{r\_ eff}}{G \cdot F}B_{EMI}}} \right)}}{B_{E} \approx {\frac{1}{F}\left( {V_{ic} + \frac{B_{harmo}}{G} + {\frac{\mu_{r\_ eff}}{G}B_{EMI}}} \right)}}} & \lbrack 5\rbrack \end{matrix}$

It is observed that if G*F>>1, the amplitudes of the harmonics are divided by the gain of the direct chain G. That said, as will be highlighted in the paragraph dealing with the modelling and filtering, the fact of measuring Xuj and of using reference signals of the induction emitted in the model of signals received, makes the filtering device insensitive to harmonics, which is a fundamental advantage relative to existing systems for which the measurement of the current in E1.1, E1.2, E1.3 is no longer the image of the induction emitted following the appearance of harmonics.

As said previously, one of the aspects of the invention consists of producing a core in order to obtain an effective relative permeability μ_(r) _(_) _(eff) of a few hundreds of units. The existence of cores of ferrite or of shims made of ferromagnetic alloy exists in a number of applications. Said latter used for example in transformers, must be laminated to reduce the Eddy currents which counter the magnetisation and cause losses. Ferrite, much more conductive than ferromagnetic alloys, makes it possible to use cores with uniform density of said matter obtained by sintering. In general, the cores are spherical or cubic (or even parallelepiped) according to FIG. 6. The magnetisation of the permeable matter of the cores subject to an excitation of magnetic field is a complex phenomenon because develops a demagnetising field that counters the excitation field. Said demagnetisation field is often explained by the creation of dummy magnetic fields on the surface of the volumes of ferromagnetic matter. Therefore, it is simply explained that the demagnetising field is closely linked to the geometry of the volume of the core and to the magnetisation. The demagnetising field can only be computed for simple examples (sphere, ellipsoids, cylinders). In the general case, approximations are made. Thus, for a sphere of material of infinite relative permeability μ_(Γ), it is shown (C. F. J. D. Jackson Classical Electrodynamics. Ed. Wiley) that the effective relative permeability μ_(r) _(_) _(eff) is at a maximum of three. For a cube, the value is of the same order of magnitude. With cubic or spherical cores, very high gains cannot be expected. It is known that for elongated cylinder-shaped bars of diameter D and length L, the demagnetising field H_(D) at the centre is −0.5*(D/L)²*M, i.e. Hd=−δ*M where the magnetisation M is of the type M=(μ_(R)−1)H, H being the magnetic field present within the material after the magnetisation, with the relation H=H₀−H_(D), H₀ being the external magnetic excitation field and δ is the demagnetising factor. Close to the edges, the demagnetising field is M/2.

From the preceding relations, a formula of the induction is deduced, for the ellipsoids of which the magnetisation is uniform,

$\begin{matrix} {{B = {{\mu_{0} \cdot \frac{\mu_{R}}{1 + {\left( {\mu_{R} - 1} \right) \cdot \delta}}}H_{0}}}{{and}\mspace{14mu} {if}}{{\mu_{R}\operatorname{>>}1},{B = {\frac{\mu_{R}}{1 + {\mu_{R} \cdot \delta}}{B_{0}.}}}}} & \lbrack 6\rbrack \end{matrix}$

In general, μ_(R)·δ>>1, therefore

$B = {{2 \cdot \left( \frac{L}{D} \right)^{2} \cdot B_{0}} = {\mu_{r} \cdot {B_{0}.}}}$

Using the preceding example of the elongated bar, this gives

$B = {{2 \cdot \left( \frac{L}{D} \right)^{2} \cdot B_{0}} = {\mu_{r} \cdot {B_{0}.}}}$

Said relation is only approximate, the value of μ_(r) is in general lower because the magnetisation is not uniform. Experimentally, the exponent is between one and two. But an increase in the induction in the order of μ_(Γ) is indeed observed in the volume of the material, but also on the outside.

Therefore, the invention consists of an arrangement of permeable bars of L/D ratio chosen so that the gain in induction μ_(r-eff)=α·μ_(r) is higher than ten. The coefficient α, lower than the unit, takes into account a plurality of factors, in particular:

-   -   the volume of magnetised material parallel with each axis of the         coils. Each axis having to have the same volume, the volume of         each one is the third of the total volume available.     -   the manner in which are wound the turns producing the excitation         field H₀.     -   the Eddy currents induced by H₀.

According to the invention, to optimise the coefficient a, very thin bars of permeable material are used, for example, wires of Mu-metal, permalloy or Vitrovac electrically isolated in advance, stored according to FIG. 7-1 in a tube of material resistant to heat treatments (silica, ceramic).

Thus, according to the at least two non-parallel transmission axes, the bars are grouped (FIG. 7-2) to form a block of square section (FIG. 7-3) or cylinder shape (FIG. 7-4) comprising a large number of bars. Said blocks 7-3 and 7-4 are arranged so as to form three volumes of orthogonal magnetisation materials and having a symmetry relative to the centre common to the three axes.

FIG. 8-a shows how the assembled blocks of FIG. 7-3 or 7-4 can be used: three windings are produced around three identical blocks that are then assembled mechanically to form three substantially perpendicular axes. Said three coils are not concentric, which poses significant difficulties for finding the position of the three-axis sensor attached to the object the position and orientation of which is to be found. Therefore, preference will be given to concentric transmitting blocks according to FIGS. 8-b and 9. In FIG. 8-b, preferable configurations of blocks are shown so that there is a centre of symmetry of the three magnetised volumes and that each axis has a magnetic moment of similar value. FIG. 4 has two projection views of a preferred device which is a generalisation of the preceding blocks: a plurality of blocks of type 2-3 are interlinked according to the three directions such that there is the best symmetry relative to a central point. According to FIG. 9 a cubic block is obtained on which three substantially orthogonal windings are arranged through which will pass the currents injected by the electronic circuits. So that the magnetic induction vector behaves in the space according to the equations of the dipole, we remain in the invention by producing a block the external surface of which is similar to a sphere, by having blocks 7-3 or 7-4 of shorter length when moving further away from the centre.

A device consisting of producing three concentric spherical coils instead of the concentric cubic coils in FIG. 9, and introducing the same overlap of blocks of type 7-3 or 7-4 in the volume of the inner coil remains within the field of the invention.

Another aspect of the invention concerns the control at zero of the quasi-static magnetisation produced by quasi static disturbances, such as for example, the earth's magnetic field. To avoid the saturation of the bars of blocks 7-3 or 7-4 in the presence of a continuous or quasi-continuous magnetisation, the symmetry of the currents circulating in the coils is detected. FIG. 10-a shows the operating principle: when a static or quasi static field Hext is present in the environment, the projection H_(D) thereof according to the transmission axis E.l offsets the point of operation of the alternating excitation field H_(i) produced by the coils according to diagram 10-b. When the offset H_(D) is zero, the difference between the peak values I₀ ⁺ and I₀ ⁻ is zero. If H_(D) is not zero, the difference between the peak values I_(D) ⁺ and I_(D) ⁻ is not zero. This is due to the non-linearity of the magnetisation curve of the ferromagnetic materials which modifies the inductance of the coil L depending on the excitation H sum of the external field H_(ext) and of the excitation Hi created by the current of the coils knowing that L=μ_(r)(H)×L₀ with L₀ inductance of the coreless coil. Exploitation of the impedance variation which deforms the current is carried out by the detection of the symmetry of the current circulating in the coil: The current through the resistance R_(IMj) is measured at point E.l.j, j=l to 3, by the impedance adapter amplifier E.5.2 the output voltage of which passes through a double peak detector E.5.1 which in a known manner detects the positive peak value I_(D) ⁺ and the negative peak value I_(D) ⁻, then the difference I_(D) ⁺−I_(D) ⁻ is filtered by a filter RC of the first conventional order the cut-off frequency of which is a few Hertz. The output V_(CRJ) of E.5.1 is then added to V_(Icj) with the sign adapted according to the direction of winding so as to cancel out the field offset H_(D). The symmetry of the current could also be detected by the creation of even harmonics of the current knowing that the symmetrical excitation Hi only has odd harmonics.

A—The On-Board Processor 4:

The computing processor is coupled with the three measurement assemblies C-1, C-2, C-3 previously described in order to firstly produce at discrete times t_(k)=k*Te the acquisition of signals on one hand by analogue/digital conversion of the second receiving assembly C-1 as well as of the third sub-assembly E.3.1 of said first transmitting assembly E, on the other hand by digital serial links of said third assembly for acquiring angular velocities C.3.1 at the frequency F_(EG) as well as the angles of attitude of said second object M relative to the absolute fixed mark delivered by C.3.2, secondly generate and produce digital/analogue conversions by the block E.4 for providing the setpoints of the control of predetermined currents in the first transmitting assembly E, thirdly, to produce the computations of a first position/orientation from a complete model of the measured inductions the variables of which are developed from the signals acquired and some parameters of which identified by optimum filtering represent the terms proportional to a dipolar or multipolar field model of which the position and orientation of the block C-1 are extracted. The block 4.3, receives, for example, from a conventional digital serial link which communicates with the inertial system of the platform, the information dated relative to the specific clock of 4 is constituted. If necessary, this makes it possible to temporally reset the attitudes of the platform. Said block also receives the serial type digital information of the MEMS inertial sensor C-3.1.

B—Method for Extracting the Noise Reference:

If the equation [1] is used,

{right arrow over (B)} _(TE) ={right arrow over (B)} _(EU) +{right arrow over (B)} _(EMI) +{right arrow over (B)} _(ECI) +{right arrow over (B)} _(FMI) +{right arrow over (B)} _(Γ)  [7]

the useful signal {right arrow over (B)}_(EU) is linearly dependent on the signals emitted by the transmitter block E. According to FIG. 4, the fields emitted by the axes El are measured by the block E3 previously described the output of which is Xu_(j). In other words, Xu_(j) is the image of the magnetic field emitted by the axis j regardless of the non-linear amplification function provided by the magnetic cores. It can be noted that the sum of the ECI and FMI noises noted B_(PCU)={right arrow over (B)}_(ECI)+{right arrow over (B)}_(FMI) (PCU for disturbances correlated with U) are the noises correlated with Xu. The earth's magnetic field is presumed to be filtered by a known conventional filter not forming part of the invention. Concerning the EMI additive noises, for one particular embodiment of the invention, same are measured by the block C-2: as indicated in FIG. 3, the block C-2 is fixed in the platform P, including a plurality of sensors installed in points such that i) the field emitted by the assembly E-1 is quasi zero or at the very least much lower than the point, contained in the volume of motion of the sensor, where C-1 of the mobile assembly M is situated, ii) the disturbance fields statistically not correlated with the fields emitted by E-1 and existing in the centre of the sensor C-1 are very strongly correlated with said fields measured by C-2. Said notions are subsequently specified.

Consequently, it will be considered that the additive noise {right arrow over (B)}_(FMI) measured in Nb points of the environment, by definition not correlated with the fields emitted estimated Xu has been noted

{right arrow over (B)} _(RM)(t _(k))={right arrow over (B)} _(SC) +{right arrow over (B)} _(R)  [8]

The signal B_(RM)(t_(k)) is shown in FIG. 4 by the analogue signals Sb which are output from the block C-2 and which are digitalised as the signals Xu_(j) and Sc_(i), j=1 to Ne, i=1 to Nc.

In some environments, such as for example aeroplanes, the noise B_(EMI) is lower than in helicopter environments and in particular the noise B_(R) is very low. In said type of environment, the noise may have to be extracted instead of being measured. The definition of the block 4.4 therefore enables a method for extracting the reference noise B_(RM)(t_(k)) in two different manners:

-   i. First method: either an extraction directly from the signal Sc     (obtained by the acquisition of the signal provided by the first     measurement assembly C-1). In this case, said choice is made by the     processor in the block 4.4 depending on the nature of the magnetic     noise. Said choice ensues from an initial analysis of the magnetic     noise of the environment when powered or at the request of the user.     For example, when powering on, in the absence of signals emitted by     the transmitting antenna, if the mean power density values of the     measured signals are harmonic and of acceptable frequency stability     (variation of 10 to 20% maximum of the mean frequency) and less than     the mean power density level of the signals due to the emission of     the transmitting antenna when same emits, said choice is made. Said     choice may also be made by the user following the accumulation of     the experience that he has obtained from the environment or any     other means. Said choice requires the transmitting power to be zero     during a period of time T_(off), said period T_(off) being     interlinked between at least one transmission period of time T_(obs)     at power not zero, with T_(off)<T_(obs)/2. Two examples are given in     FIG. 11. Over the period T_(OFF) the stationary disturbance signals     (low variability over T_(OBS)) are identified in the same manner as     same that will be described for the extraction of said same signals     on the signal Sb. The model of these signals B_(sc) or B_(ESC) (the     letter _(E) indicates that said vector is expressed in the     transmitter mark)

$\begin{matrix} {{B_{SC}\left( {i_{c},t_{k}} \right)} = {{\sum\limits_{k_{sc} = 1}^{N_{sc}}{{{\hat{C}}_{SC}^{re}\left( {i_{c},k_{sc}} \right)} \cdot {\cos \left( {\omega_{k_{sc}}t_{k}} \right)}}} + {{{\hat{C}}_{SC}^{im}\left( {i_{c},k_{sc}} \right)} \cdot {\sin \left( {\omega_{k_{sc}}t_{k}} \right)}}}} & \lbrack 9\rbrack \end{matrix}$

the frequencies ω_(k) _(sc) of which are estimated (by methods of the FFT type or preferably by methods of the High Resolution type). The coefficients are identified up to T_(off).

As another example, two periods T_(OFF) can be considered according to FIG. 11 outlining the period of transmission T_(ON) to produce a linear interpolation of the parameters Ĉ_(SC) ^(re)(i_(c),k_(sc)) and Ĉ_(SC) ^(im)(i_(c),k_(sc)). The output information is therefore offset from Ton, but said time may be very short if a HR (High Resolution) method is used to identify the equation [9].

The independent variables X_(C)(t_(k))=cos(ω_(k) _(sc) (t_(k))) and X_(S)(t_(k))=sin(ω_(k) _(sc) (t_(k))) are deduced therefrom during the period T_(ON). Said variables can be grouped under the term of X_(sc) which becomes a matrix [N_(obs),2] where N_(obs) is the number of samples acquired during Ton: Nobs=Ton*Fe. Said variables are added to the variables Xu_(j) to form a model relatively linear to said independent variables X_(UJ), X_(sc). Each component i_(c) of the sensor C-1 may be written as follows if B_(R) is negligible:

B _(F) ={circumflex over (B)} _(EC)(i _(c) ,t _(k))+{circumflex over (B)} _(RM)(i _(c) ,t _(k))  [10]

With

$\begin{matrix} {{{\overset{\Cap}{B}}_{EC}\left( {i_{c},t_{k}} \right)} = {\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{i_{c}} = 0}^{N_{i_{c}}}{{{\hat{A}}_{C}\left( {i_{c},j,k_{i_{c}}} \right)} \cdot {X_{C}\left( {i_{c},j,k_{i_{c}}} \right)}}}}} & & \lbrack 11\rbrack \end{matrix}$

where X_(C)(j,k_(i) _(c) ,t_(k))=X_(Uj)(t_(k)−k_(i) _(c) T_(c)) [10] is written:

$\begin{matrix} {B_{E} = {{\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{i_{c}} = 0}^{N_{i_{c}}}{{{\hat{A}}_{C}\left( {i_{c},j,k_{i_{c}}} \right)} \cdot {X_{C}\left( {i_{c},j,k_{i_{c}}} \right)}}}} + {\sum\limits_{k_{sc} = 1}^{N_{sc}}{{{\hat{C}}_{SC}^{re}\left( {i_{c},k_{sc}} \right)} \cdot {\cos \left( {\omega_{k_{sc}}t_{k}} \right)}}} + {{{\hat{C}}_{SC}^{im}\left( {i_{c},k_{sc}} \right)} \cdot {\sin \left( {\omega_{k_{sc}}t_{k}} \right)}}}} & \left\lbrack {10\text{-}{bis}} \right\rbrack \end{matrix}$

It is noted that X_(C)(j,k_(i) _(c) ,t_(k)) are the values offset over time of the fields emitted by the transmitter on each axis j and for each component i_(c) of the sensor of the block C-1. In a way, the estimator is a transversal filter which is justified by the fact that the ECI and FMI disturbances may be considered as the output of filters substantially of the first order of which the input are the signals X_(Uj)(t_(k)).

The indexes K_(ic) are relative to the delays of the independent variables of the model and range from 0 to N_(ic), said latter index N_(ic) being defined strictly necessary in order to minimise the residual error. The offset terms of K_(ic) form a transversal filter. B_(RM) is written in the form of a development of complex variables:

$\begin{matrix} {{{{\hat{B}}_{RM}\left( {i_{c},t_{k}} \right)} \cong {{\hat{B}}_{SC}\left( {i_{c},t_{k}} \right)}} = {\sum\limits_{k_{sc} = 1}^{N_{sc}}{{{\hat{C}}_{SC}\left( {i_{c},k_{sc}} \right)} \cdot {X_{sc}\left( t_{k} \right)}}}} & \lbrack 12\rbrack \end{matrix}$

The equations [11] and [12] which are linear relative to the parameters to be estimated.

If a model was produced for X_(sc)(t_(k)) of the same type as [11] i.e. a development sum of the type [12] for each variable X_(sc)(t_(k)k_(sc)·T_(c)), this would remain within the field of the invention. The same would apply if the complex parameters Ĉ_(SC)(i_(c),k_(sc)) were no longer constant but depended on the time in the form of a polynomial of the time

${{\hat{C}}_{SC}\left( {i_{c},k_{sc},t_{k}} \right)} = {\sum\limits_{{io} = 0}^{{io} = N_{io}}{{C_{io}\left( {i_{c},k_{sc}} \right)} \cdot {t_{k}^{io}.}}}$

For said temporal model, the values of the terms C_(io)((i_(c)k_(sc))·_(k) ^(io) are computed by developing same in [12]. Any type of different temporal model no longer comprising of temporal polynomial but of sums of functions of the time of exponential type e^(a·t) or e^(ibt) (complex periodic function

i²=−l) remains within the field of the invention.

The parameters of said model are determined by a conventional method of least squares (MSE) or an equivalent recursive method (LMS, RLS). The estimation of the parameters relative to the variables Xu_(j) may be refined by subtracting the term {circumflex over (B)}_(SC)(i_(c),t_(k)) estimated at the signal Ŝc(i_(c),t_(k)). The new estimation makes it possible to estimate the correlated terms with better accuracy after one or two iterations. The reference noise {circumflex over (B)}_(RM) is in this case the signal {circumflex over (B)}_(SC′) estimated in the preceding iteration.

-   ii. Second method: The continuous measurement of disturbance signals     by S_(b) may be essential in the presence of very strong harmonic     signals of non-constant amplitudes and frequencies up to Tobs but     also in the presence of non-stationary deterministic disturbances or     random disturbances. I.e. an estimation of the signals radiated by     the measurement of the signals S_(b). As written and illustrated in     FIG. 4, the signal noted S_(b) consists of signals coming from at     least one magnetic sensor of one to three orthogonal axes for     measuring the magnetic fields between the continuous and a few KHz     (fluxgate sensor, fluxmeter, AMR, GMR, TMR, etc.), said sensors     being attached to said second object in at least Nb points, measure     the vector sum of the magnetic inductions present in said Nb points     of the environment, sufficiently far enough away from the first     transmitting assembly so that said assembly constitutes a noise     reference B_(RM)(t_(k)) by preferentially measuring the magnetic     inductions independent of the inductions generated by the first     transmitting assembly E1, and this produced without interruption     (T_(off)=0).

The measurements of the additive noise B_(EMI) are identified by the output signals S_(b) of the block C-2 in diagram 4. In a particular embodiment, in order to facilitate the drafting, Nb=1 will be taken and it will be considered that the measurement of a single component is sufficient. The measurement of {circumflex over (B)}_(RM)(t_(k)) according to a particular direction will be noted to be considered as a signal very strongly correlated with B_(EMI). In the ideal situation, the measured noise reference B_(RM) contains no signal correlated to Xu_(j), j=l to 3. In practice, it is very difficult to arrange sensors C-2 at locations such that no component correlated with X_(U) exists, including and in particular the signals B_(ECI) and B_(FMI). Therefore, the signal for measuring the noise S_(b) consisting of the same components as the signal S_(c) must be considered. Therefore, the same problem arises as in i), i.e. that the various components of the signal S_(b) must be identified that are written as follows:

B _(C2) =B _(RU) +B _(RM)  [13-a]

with B _(RU) =B _(u) +B _(PCU)  [13-b]

where B_(U) is linearly dependent on X_(Uj)(t_(k)), B_(PCU) is linearly dependent on X_(Uj)(t−k·Te)

and B _(RM) =B _(SC) +B _(R)  [14]

is the term not correlated with X_(Uj).

B_(RM) is not negligible as in i) and this consists of extracting from [13-a] the portion B_(RM). As in the case i), all of the terms of the model must be identified to prevent biasing the estimation of the parameters of the model. However, the random signal B_(R) is in general weaker than B_(sc) and Bcu, and the identification may be performed over longer times insofar as the sensors of C-2 are immobile. It can also be considered that, since the transmitter and the sensor(s) of the block C-2 are fixed on the same structure, the identification of the parameters of the model [14] may be carried out once for all or indeed at the start of use of the system during an initialisation phase of sufficient duration in order to enable very good accuracy in the estimation of the parameters following filtering of the terms of [14] which are not correlated with [14]. Said identification is exactly the same as that described in [10], [11], [12]. The parameters of [14] are therefore stored in memory for the computation of {circumflex over (B)}_(CU). The principle of extraction of B_(RM) consists of writing:

{circumflex over (B)} _(RM) =B _(C2) −{circumflex over (B)} _(RU)  [16-a]

where B_(RU) are the estimates of the signals correlated with Xu_(j).

After the identification of the model of the type:

$B_{E} = {{\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{i_{c}} = 0}^{N_{i_{c}}}{{{\hat{A}}_{C}\left( {i_{c},j,k_{i_{c}}} \right)} \cdot {X_{C}\left( {i_{c},j,k_{i_{c}}} \right)}}}} + {\sum\limits_{k_{sc} = 1}^{N_{sc}}{{{\hat{C}}_{SC}^{re}\left( {i_{c},k_{sc}} \right)} \cdot {\cos \left( {\omega_{k_{sc}}t_{k}} \right)}}} + {{{\hat{C}}_{SC}^{im}\left( {i_{c},k_{sc}} \right)} \cdot {\sin \left( {\omega_{k_{sc}}t_{k}} \right)}}}$

All of the terms of the signals correlated with Xu_(j) are extracted therefrom to form the signal {circumflex over (B)}_(RU):

$\begin{matrix} {{{\overset{\Cap}{B}}_{RU}\left( {i_{c},t_{k}} \right)} = {\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{b} = 0}^{N_{b}}{{{\overset{\Cap}{A}}_{BRC}\left( {i_{c},j,k_{b}} \right)} \cdot {X_{C}\left( {i_{c},j,k_{b}} \right)}_{\;}}}}} & \left\lbrack {16\text{-}b} \right\rbrack \end{matrix}$

{circumflex over (B)}_(RM′) of [16-a] is therefore the estimate of the noise not correlated with the emitted fields.

It is therefore noted that when there is emission of signals by E-1, in the two embodiments i) and ii) previously described, the same model should be identified on the measurements Sc (coming from the block C-1) or S_(b) (coming from the block C-2).

The model of the signal to be identified within the framework of said second embodiment of the invention for which a measurement of the EMI noise is taken and of which only the BRM noise is extracted, is therefore produced.

The model of Bc is developed which is the field measured by the sensor C-1:

{right arrow over (B)} _(C) =R _(c/i) ¹({right arrow over (B)} _(U/E) +{right arrow over (B)} _(CU/E)+{right arrow over ({circumflex over (B)})}_(RM/E))  [17]

In the index _(U/E), _(E) indicates that the vector is expressed in the mark of the transmitter (said index is sometimes omitted by simplifications knowing that the context indicates in which mark the fields are expressed), _(U) indicates that this is the portion of the field linearly dependent on the fields emitted by the transmitter X_(U). The index C_(U) indicates that {right arrow over (B)}_(CU/E)={right arrow over (B)}_(ECI)+{right arrow over (B)}_(FMI) represents the vector of the disturbances correlated with the vector X_(U). {right arrow over (B)}_(CU/E) could be modelled by the convolution of {right arrow over (B)}_(U/E) by the impulse response of the complex filter existing between the two magnitudes. {right arrow over ({circumflex over (B)})}_(RM/E) has the same meaning as in [13] and [15], it is the noise present in the environment not correlated with the emitted fields.

B_(T) is overlooked which is presumed to be filtered by a conventional digital filter known by the person skilled in the art. The three models are developed linearly relative to the parameters to be identified for example by a conventional square error minimisation method. When the coefficients are determined, the nine terms (3 terms due to each transmission channel for each component of the triaxial sensor C-1) are extracted relative to X_(U)(t_(k)) components of the matrix noted A which will be better defined subsequently. The fundamental interest of said complete modelling of the signals received by the sensor C-1 lies in the fact that the 9 parameters of A are even less biased if the independent variables of the model more accurately represent the physical phenomena.

The following three models of [17] are developed: Model {right arrow over (B)}_(U/E), Model {right arrow over (B)}_(CU/E), Model {right arrow over (B)}_(RMI/E):

Model {right arrow over (B)}_(U/E):

Consequently, it is considered that the sensor C-1 has been corrected of the errors thereof according to known methods: the functions of gain correction, misalignment, etc., are applied. Presuming that the distance between the sensor C-1 and transmitter is at least three times the largest dimension of the transmitter, it is therefore written in a known manner that the model is of dipolar type and is written

$\begin{matrix} {{B_{C}(t)} = {{{{\left\lbrack {R_{c/e}(t)} \right\rbrack^{t}\;\lbrack P\rbrack}^{t}\lbrack H\rbrack}\;\lbrack P\rbrack}\; \left( {{M_{1}{f_{1}(t)}} + {M_{2}{f_{2}(t)}} + {M_{3}{f_{3}(t)}}} \right)}} & \lbrack 18\rbrack \\ {H = \frac{\begin{bmatrix} 2 & 0 & 0 \\ 0 & {- 1} & 0 \\ 0 & 0 & {- 1} \end{bmatrix}}{D_{C/E}^{3}}} & \lbrack 19\rbrack \end{matrix}$

D_(c/E) is the distance between the centre O_(C) of the sensor C-1 and the centre of the transmitter O_(e):

O _(E) {right arrow over (O)} _(C)

D _(C/E) ·{right arrow over (u)},  [19-bis]

D_(C/E) is variable as a function of time, like the rotation R_(C/E)(t:={right arrow over (u)}: unit vector of O_(E){right arrow over (O)}_(C) expressed in the reference mark of the transmitter R_(E) which is mechanically defined in a known manner by the person skilled in the art relatively to the mark of the platform R_(p) according to FIG. 2.

P is the transfer matrix between the mark of the transmitter and the mark ({right arrow over (u)},{right arrow over (v)},{right arrow over (w)}) with {right arrow over (w)}={right arrow over (u)}_(M)̂{right arrow over (u)} and {right arrow over (v)}={right arrow over (w)}̂{right arrow over (u)} and known as the radial mark, where {right arrow over (u)}_(M) is the unit vector of a transmission axis. It is also shown that for example:

$\begin{matrix} {{{{{{{{If}\mspace{14mu} \overset{\rightarrow}{u}} =}}\begin{matrix} x & \; & \; \\ y & {then} & {\overset{\rightarrow}{v} = \frac{1}{\sqrt{y^{2} + z^{2}}}} \\ z & \; & \; \end{matrix}}}\begin{matrix} {- \left( {y^{2} + z^{2}} \right)} \\ {xy} \\ {xz} \end{matrix}},} & \lbrack 20\rbrack \\ {{{{\overset{\rightarrow}{w} = \frac{1}{\sqrt{y^{2} + z^{2}}}}}\begin{matrix} 0 \\ {- z} \\ y \end{matrix}}{and}} & \; \\ {P = \begin{bmatrix} \overset{\rightarrow}{u} & \overset{\rightarrow}{v} & \overset{\rightarrow}{w} \end{bmatrix}} & \lbrack 21\rbrack \\ {{{In}\mspace{14mu}\lbrack 18\rbrack},} & \; \\ {{{{{{{{{M_{1} = {m_{1}{f_{1}(t)}}}}\begin{matrix} \alpha_{1} \\ \beta_{1} \\ \gamma_{1} \end{matrix}\mspace{31mu} M_{2}} = {m_{2}{f_{2}(t)}}}}\begin{matrix} \alpha_{2} \\ \beta_{2} \\ \gamma_{2} \end{matrix}\mspace{31mu} M_{1}} = {m_{3}{f_{3}(t)}}}}\begin{matrix} \alpha_{3} \\ \beta_{3} \\ \gamma_{3} \end{matrix}} & \lbrack 22\rbrack \end{matrix}$

are the dipolar moments of the transmitting coils the amplitude of which change substantially over time according to the functions f_(j)(t), f₂(t), f₃(t) imposed by the currents circulating in the coils.

m₁ m₂, m₃ are the multiplicative terms of amplitudes of the magnetic moments that depend on the units chosen, the gains of the current amplifiers E-2, α_(i),β_(i),γ_(i) the direction coefficients (cosines) of the collinear unit vectors of the magnetic moments (axes of revolution) of the coils, f₁(t), f₂(t), f₃(t) represent the variations of the standardised measurements proportional to the magnetic inductions emitted over time by each transmitting coil. The measurements of said emitted inductions are taken by the sensors E-3 secured to the transmitter E in FIG. 4 and are proportional to _(L). The output V_(E3) of the sensors E-3 is either digitalised by the CAN block of the processor for the three axes and digitally incorporated into or indeed according to a preferred mode of embodiment according to FIG. 4, it is first incorporated by an analogue amplifier E-3-2 then digitalised by the CAN 4-1 of the processor 4 and each of the channels is standardised by a coefficient determined in the factory in a manner known by the person skilled in the art, such that the values thus standardised correspond to the physical units and to the nominal values thereof. The coefficients α_(i),β_(i),γ_(i) are determined in the factory by calibration procedures on factory test bench using methods known by the person skilled in the art.

The functions {right arrow over (X)}_(U)=[X_(U1),X_(U2),X_(U3)]^(t) thus digitalised, proportional to the functions f₁(t), f₂(t), f₃(t) are therefore the images of the fields emitted by the 3 coils: by re-writing [18], if {right arrow over (x)}_(p) is the vector {right arrow over (O_(E)O_(C))}

B _(C)(t)=[R _(c/e)(t)]^(t) B({right arrow over (x)} _(p))[M ₁ X _(U1)(t)+M ₂ X _(U2)(t)+M ₃ X _(U3)(t)]

B({right arrow over (x)} _(p))=[P][H][P)]^(t)  [23]

Or again if it is noted

A=[R _(c/e)(t)]^(t) B({right arrow over (x)} _(p))  [23-bis]

$\begin{matrix} \left. {{{{{{{{Bc}(t)} = {{{\lbrack A\rbrack \cdot \left\lbrack {{X_{U\; 1}(t)} \cdot m_{1} \cdot} \right.}\begin{matrix} \alpha_{1} \\ \beta_{1} \\ \gamma_{1} \end{matrix}} + {{X_{U\; 2}(t)} \cdot m_{2} \cdot}}}}\begin{matrix} \alpha_{2} \\ \beta_{2} \\ \gamma_{2} \end{matrix}} + {{X_{U\; 3}(t)} \cdot m_{3} \cdot}}}\begin{matrix} \alpha_{3} \\ \beta_{3} \\ \gamma_{3} \end{matrix}} \right\rbrack & \lbrack 24\rbrack \\ {{{Bc}(t)} = \begin{bmatrix} {{\left( {{A_{11}\alpha_{1}} + {A_{12}\beta_{1}} + {A_{13}\gamma_{1}}} \right)m_{1}{f_{1}(t)}} + {\left( {{A_{11}\alpha_{2}} + {A_{12}\beta_{2}} + {A_{13}\gamma_{2}}} \right)m_{2}{f_{2}(t)}} + {\left( {{A_{11}\alpha_{3}} + {A_{12}\beta_{3}} + {A_{13}\gamma_{3}}} \right)m_{3}{f_{3}(t)}}} \\ {{\left( {{A_{21}\alpha_{1}} + {A_{22}\beta_{1}} + {A_{23}\gamma_{1}}} \right)m_{1}{f_{1}(t)}} + {\left( {{A_{21}\alpha_{2}} + {A_{22}\beta_{2}} + {A_{13}\gamma_{2}}} \right)m_{2}{f_{2}(t)}} + {\left( {{A_{21}\alpha_{3}} + {A_{22}\beta_{3}} + {A_{33}\gamma_{3}}} \right)m_{3}{f_{3}(t)}}} \\ {{\left( {{A_{31}\alpha_{1}} + {A_{32}\beta_{1}} + {A_{33}\gamma_{1}}} \right)m_{1}{f_{1}(t)}} + {\left( {{A_{31}\alpha_{2}} + {A_{32}\beta_{2}} + {A_{33}\gamma_{2}}} \right)m_{2}{f_{2}(t)}} + {\left( {{A_{31}\alpha_{3}} + {A_{32}\beta_{3}} + {A_{33}\gamma_{3}}} \right)m_{3}{f_{3}(t)}}} \end{bmatrix}} & \left. 25 \right\rbrack \end{matrix}$

This gives three equations to each three unknowns, i.e. 9 terms to be identified. Measuring the three components of Bc, when there are no disturbances B_(CU) and B_(RM) of [17], the nine terms of {right arrow over (X)}_(U)=[X_(U1),X_(U2),X_(U3)]^(t) are identified using a conventional least square method (MSE) or an equivalent recursive method (LMS, RLS).

Therefore, the matrix W is obtained which can be applied in the form of:

$\begin{matrix} {{W = {{\begin{bmatrix} A_{11} & A_{12} & A_{13} \\ A_{21} & A_{22} & A_{23} \\ A_{31} & A_{32} & A_{33} \end{bmatrix}\begin{bmatrix} \alpha_{1} & \alpha_{2} & \alpha_{3} \\ \beta_{1} & \beta_{2} & \beta_{3} \\ \gamma_{1} & \gamma_{2} & \gamma_{3} \end{bmatrix}}\begin{bmatrix} m_{1} & 0 & 0 \\ 0 & m_{2} & 0 \\ 0 & 0 & m_{3} \end{bmatrix}}}{{i.e.\mspace{14mu} W} = {\lbrack A\rbrack C_{E}K_{E}}}} & \lbrack 26\rbrack \end{matrix}$

The two matrices, C_(E) and K_(E) (gains and misalignments) relative to the transmitting block E-1, are identified in the factory, therefore the matrix A sought is easily obtained.

[A]=W[C _(E) K _(E)]⁻¹  [27]

Knowing A, the position {right arrow over (x)}_(p) of the centre of the sensor in the transmitter mark and the rotation R_(C/E) (or direction cosines of the axes of the sensor in the transmitter mark) are obtained according to the methods of prior art. Through the identification of the matrix

A consisting of the coefficients of the functions {right arrow over (X)}_(CU)=[X_(U1),X_(U2),X_(U3)]^(t), the demultiplexing of the transmitting channels was thus carried out by identification of a model, and not by temporal demultiplexing (emissions not simultaneous), or by frequential demultiplexing (U.S. Pat. No. 6,754,609 Lescourret, U.S. Pat. No. 6,172,499 ASHE, etc.) or any other demultiplexing.

MODEL {right arrow over (B)}_(CU/E):

As already seen, {right arrow over (B)}_(CU/E), may be considered as the output of a linear filter the input of which are the inductive fields emitted by El, and the output is the measurement by the sensor C-1. It is therefore still possible to consider that the output at instant t_(k) is a linear combination of the inputs at instants t_(k)−k_(l)·Te. If it is noted: {right arrow over (X)}_(CU)(t_(k)−k₁T_(e))=[X_(U1)(t_(k)=k₁T_(e)),X_(U2)(t_(k)−k₁T_(e)),X_(U3)(t_(k)−k₁T_(e))]^(t), for each component i_(c) (i_(c)=l to 3) of the sensor C-1, the following model is formed:

$\begin{matrix} {{B_{{CU}/E}\left( {i_{c},t_{k}} \right)} = {\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{{k{(i_{c})}} = 0}^{N{(i_{c})}}{{A_{cu}\left( {i_{c},j,k_{i_{c}}} \right)}{X_{cu}\left( {j,{t_{k} - {{k\left( i_{c} \right)}{Te}}}} \right)}}}}} & \lbrack 28\rbrack \end{matrix}$

In general, in the environments of cockpits, there are practically no ferromagnetic materials, the FMI effects are therefore low in particular for the high frequencies and in addition vary substantially in 1/(D_(P/E) ³D_(C/P) ³) where D_(P/E) is the transmitter-disturber distance and D_(C/p) the disturber-sensor C-1 distance. When it is possible to ignore same, the ECI disturbers are the only disturbers of which the model can be written as a function of the shifts of the emitted fields:

$\begin{matrix} {{\overset{\rightarrow}{X_{CU}}\left( {t_{k} - {k_{1}T_{e}}} \right)} = \left\lbrack {{X_{U\; 1}^{\prime}\left( {t_{k} - {k_{1}T_{e}}} \right)},{X_{U\; 2}^{\prime}\left( {t_{k} - {k_{1}T_{e}}} \right)},{X_{U\; 3}^{\prime}\left( {t_{k} - {k_{1}T_{e}}} \right)}} \right\rbrack^{t}} & \lbrack 29\rbrack \\ {\mspace{79mu} {With}} & \; \\ {\mspace{79mu} {{X_{Uj}^{\prime}\left( t_{k} \right)} \approx \frac{\left( {{X_{Uj}\left( t_{k} \right)} - {X_{Uj}\left( {t_{k} - T_{e}} \right)}} \right)}{Te}}} & \; \end{matrix}$

MODEL {right arrow over (B)}_(RM/E):

The reference noise is extracted from the signals Sb is {circumflex over ({right arrow over (B)})}_(RM)={right arrow over (B)}_(C2)−{circumflex over ({right arrow over (B)})}_(CU). If the variable is called X_(BR)(t_(k))−{circumflex over ({right arrow over (B)})}_(RM)(t_(k)), and to take into account the transfer functions between sensors, the model of the ambient noise for each component i_(c) of the sensor C-1: B_(EMI)(i_(c),t_(k)), may be applied in the form of a function of the variables X_(BR)(t_(k)−k_(b)T_(e)):

$\begin{matrix} {{{\hat{B}}_{RM}\left( {i_{c},t_{k}} \right)} = {\sum\limits_{k_{b} = 0}^{k_{b} = {N_{kb}{(i_{c})}}}{{C_{b}\left( {k_{b},i_{c}} \right)}{X_{BR}\left( {t_{k} - {k_{b}T_{e}}} \right)}}}} & \lbrack 30\rbrack \end{matrix}$

Complete Model:

The complete model [17] is written for each component of

$\begin{matrix} {{B_{C}\left( {i_{c},t_{k}} \right)} = {{\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{{k{(i_{c})}} = 0}^{N{(i_{c})}}{{A_{CU}\left( {i_{c},j,k_{i_{c}}} \right)}{X_{cu}\left( {j,{t_{k} - {{k\left( i_{c} \right)}{Te}}}} \right)}}}} + {\sum\limits_{k_{b} = 0}^{k_{b} = {N_{kb}{(i_{c})}}}{{C_{b}\left( {k_{b,}i_{c}} \right)}{X_{BR}\left( {t_{k} - {k_{b}T_{e}}} \right)}}}}} & \lbrack 31\rbrack \end{matrix}$

The number of coefficients and the number of variables are in the number of Ne*Max_(/ic)(N(i_(c))).

The nine terms of A_(cu)(i_(c),j,0) are the terms of the model in free space, i.e. without disturbers.

Once all of the coefficients are estimated using a conventional least squares method (MSE) or an equivalent recursive method (LMS, RLS, KALMAN, etc.) at each transmission cycle Tobs, the terms A_(cu)(i_(c),j,0) relative to the variables X_(Uj)(t_(k)) form a 3×3 matrix identical to W of [26] and which are the coefficients of the model in free space, since same only represent the inductive fields. As indicated above the first position and orientation are deduced therefrom at instants t_(k) from the magnetic detector insensitive to disturbances. The insensitivity to disturbances arises from the fact that the invention implements a complete model of useful signals and measured and estimated noises, a model for which the coefficients are not biased due to the completeness of the model.

The P/O_(EM) information according to FIG. 12 of the insensitive magnetic orientation and position tracker system known as IM tracker i.e. the position of the centre of the sensor X_(C/E)(t_(n)) and the rotation R_(C/E)(t_(n)) of the sensor C-1 are known at instants t_(n)=n*T_(obs), n being a positive integer: effectively, the identification of the coefficients of the equation [31] being carried out by the computing block 4-4 is performed on N_(obs) points acquired at instants t_(k) with t_(n)−t_(n−1)=T_(obs). The latency of the information provided is of T_(obs)/2.

C—Inertial and Magnetic Hybridisation

One of the aims of the invention is presented hereafter which consists of compensating the latency of a position/orientation tracker system. The example described concerns a magnetic system but would be applied to any system for detecting the orientation of a mobile body.

When the signal-to-noise ratio input from the magnetic detection system is not sufficient, either that noise exists that is not taken into account by the model or that noise is added on the sensor C-1, one method consists of increasing the number of points to further average the noise. Therefore, the latency is increased, which is relatively harmful for the piloting of aircraft. One aspect of the invention is to associate with the magnetic detection an inertial system the excellent short-term properties of which are known, i.e. a very short response time, but having long-term shifts, in particular due to bias and bias shifts. The magnetic tracker means has an excellent long-term stability but a response time related to the signal-to-noise ratio which may be insufficient in some conditions. The principle of the invention consists of associating, also called hybridising, the magnetic system and the inertial system, when the platform has an inertial unit providing the attitude of the platform at any instant within a fixed inertial reference frame. FIG. 12-a indicates prior art which consists of using the angular velocities measured on the mobile object and also on the platform in order to be processed in a KALMAN filter. FIG. 12-b describes the principle of the invention which consists of measuring the angular velocities of the mobile object M, and digitally incorporating same in a known manner from time t_(i) (initial time) to time t_(f) (final time) to obtain the rotation of the mobile between said two instants in the fixed mark. The acquisition of angular velocities is carried out by the block C-3-1 in FIG. 3, consisting of an MEMS sensor delivering digitalised angular velocities at a specific speed T_(g) which is a sub-multiple of T_(obs): T_(g)=T_(obs)/k_(g), k_(g) is a positive integer, t_(i) is for example the fraction of time that follows the instant of arrival of the information from the magnetic tracker means t_(n) i.e. t_(n) ⁺. t_(f) is the instant for which the information is desired. In the invention, there are two specific instants t_(f). The first is the instant t, the second is the instant t_(n)+T_(obs). This will be better understood later.

The rotation thus computed from the initial attitude of the gyrometric sensors C-3-1 at time t_(i) is expressed within the fixed inertial reference frame shown by the mark R_(i) in FIG. 2.

The information from the IM tracker means is available at the output of 4-4 and constitutes the first orientation known as Rot (t_(n)=n·Tobs). Said rotation is R_(C/E) ^(EM)(t_(n)), i.e. the rotation of the axes of the mark R_(M) connected to the mobile object M according to FIG. 2 expressed in the mark of the transmitter. Knowing the transfer matrix from the transmitter to the platform R_(E/P) by a measurement during installation of the transmitter in the platform and the transfer matrix of R_(M) at the mark of the sensor C-1: R_(C1), the person skilled in the art knows how to compute the rotation of the mark R_(M) relative to R_(P) i.e. R_(M/P) ^(EM). To process the magnetic and inertial information, it is necessary to express same in the same mark, for example, the mark R_(i). Therefore, R_(M/I) ^(EM)=R_(P/I)R_(M/P) ^(EM) must be computed. For this, it is necessary to know R_(P/I) which is none other than the direction cosine matrix of the platform which is provided by the inertial unit C-3-2 of the platform, in general in the form of three Euler angles, Yaw ψ, Pitch Θ and Roll φ, from which, R_(P/I) then R_(M/I) ^(EM) are computed.

The direction cosines of the gyrometers are deduced therefrom in the inertial frame at time t_(i)=t_(n) by the formula:

R _(g/i) ^(EM)(t _(n))={circumflex over (R)} _(P/i)(t _(n))·R _(M/P) ^(EM)(t _(n))·R _(g/m)  [32]

where R_(g/m) is the constant matrix defining the direction cosines of the gyrometers in the mobile mark M. The quaternion Q(t_(n)) is deduced from R_(g/i) ^(EM)(t_(n)).

The quaternion Q(t_(kg)=t_(n)−k_(g)T_(g)) obtained by digital incorporation of the equation of the type {dot over (Q)}=F(ω)Q or in the incorporated form thereof:

$\begin{matrix} {{\hat{Q}\left( t_{kg} \right)} = {\int_{t_{n}}^{t_{kg} = {t_{n} + {k_{g} \cdot T_{g}}}}{\frac{{F\left( {\overset{\hat{\rightarrow}}{\omega}(u)} \right)} \cdot {Q(u)}}{2} {of}\mspace{14mu} {the}}}} & \left\lbrack {33\text{-}a} \right\rbrack \end{matrix}$

With the initial condition:

{dot over (Q)}(t _(n))={circumflex over (Q)} _(i)(t _(n))  [33-b]

It will be seen that said initial conditions is the value of the state predicted by the model at t_(n) to which is added a fraction of the error between estimated measurement and real measurement.

$\begin{matrix} {{F\left( {\overset{\hat{\rightarrow}}{\omega}(u)} \right)} = \begin{pmatrix} 0 & {- {{\hat{\omega}}_{x}(u)}} & {- {{\hat{\omega}}_{y}(u)}} & {- {{\hat{\omega}}_{z}(u)}} \\ {{\hat{\omega}}_{x}(u)} & 0 & {+ {{\hat{\omega}}_{z}(u)}} & {- {{\hat{\omega}}_{y}(u)}} \\ {{\hat{\omega}}_{y}(u)} & {- {{\hat{\omega}}_{z}(u)}} & 0 & {+ {{\hat{\omega}}_{x}(u)}} \\ {{\hat{\omega}}_{z}(u)} & {+ {{\hat{\omega}}_{y}(u)}} & {- {{\hat{\omega}}_{x}(u)}} & 0 \end{pmatrix}} & \left\lbrack {33\text{-}c} \right\rbrack \end{matrix}$ Where {right arrow over ({circumflex over (ω)})}={right arrow over (ω)}_(m)−{right arrow over (δ{circumflex over (ω)})},  [33-d]

calculated from the values provided by the gyrometers and corrected of the errors of the gyrometers {right arrow over (δ{circumflex over (ω)})} estimated by an optimal estimator of the Kalman type (extended: EKF or “unscented”: UKF) or sub-optimal (“Recursive least squares” of the type LMS, RLS, etc.) according to a model of errors of the type

{right arrow over (δ{circumflex over (ω)})}={right arrow over (b)} _(ω) +ΔK·{right arrow over ({circumflex over (ω)})}  [34]

where ω_(b) is a random bias and K the matrix of gain, misalignment and coupling errors between channels.

The propagation of gyrometric errors is carried out by a dynamic model of the terms of {right arrow over (δ{circumflex over (ω)})}, same incorporated as is known to be carried out with a KALMAN filter. By calling dQ the error between the value Q_(i) ^(EM)(t_(n)) computed by the magnetic tracker means at time t_(n) and Q(t_(n)) incorporated from t to t_(n), the propagation state vector of the errors is for example of the type

$\begin{matrix} {X = {\begin{bmatrix} Q^{t} & {dQ}^{t} & b_{\omega}^{t} & {\Delta \; K^{t}} \end{bmatrix}^{t}:{\overset{.}{Q}\frac{1}{2}{F\left( {\overset{\hat{\rightarrow}}{\omega}}_{(t)} \right)}{Q(t)}}}} & \lbrack 35\rbrack \\ {{d\hat{\overset{.}{Q}}} = {{\frac{1}{2}{F\left( \hat{\omega} \right)}d\hat{Q}} + {\frac{1}{2}{C\left( \hat{Q} \right)}\overset{\_}{\delta\omega}}}} & \lbrack 36\rbrack \\ {{\overset{.}{\overset{\rightarrow}{b}}}_{\omega} = {{{Vg}\mspace{14mu} {ou}\mspace{14mu} {\overset{.}{\overset{\rightarrow}{b}}}_{\omega}} = {{{- \frac{1}{Tg}}{\overset{\rightarrow}{b}}_{\omega}} + {Vg}}}} & \lbrack 37\rbrack \\ {{\Delta \overset{.}{K}} = {{V_{K}\mspace{14mu} {ou}\mspace{14mu} \Delta \overset{.}{K}} = {{{- \frac{1}{T_{k}}}\Delta \; K} + V_{K}}}} & \lbrack 38\rbrack \\ {\hat{Y} = {d\hat{Q}}} & \left\lbrack {39\text{-}a} \right\rbrack \end{matrix}$ Y=dQ+v measures  [39-b]

With

$\begin{matrix} {{C(Q)} = \begin{bmatrix} {- Q_{1}} & {- Q_{2}} & {- Q_{3}} \\ {+ Q_{0}} & {- Q_{1}} & {+ Q_{2}} \\ {+ Q_{3}} & {+ Q_{0}} & {- Q_{1}} \\ {{- Q}\; 2} & {+ Q_{1}} & {+ Q_{0}} \end{bmatrix}} & \lbrack 40\rbrack \end{matrix}$

v, Vg, Vk are superimposed additive Gaussian noises centred according to the characteristics of the fluctuations of the terms {right arrow over (b)}_(ω) and K of [38-a and 38-b] and the error provided by the magnetic detection system.

Equations [35] to [38] may be digitally incorporated in various manners or be applied in the form of recurrent matrix equations. At each instant t_(n), the parameters of {right arrow over (δω)} are reset using formulas known by the person skilled in the art depending on the filter chosen, for example the KALMAN filter.

In this hypothesis, the resetting formula is of the type:

X(t _(n) ⁺)=X(t _(n) ⁻)+K _(n)(Y−Ŷ)  [41]

If the KALMAN filter (of the standard or extended (EKF) or unscented (UKF) type is used, K_(n) is obtained using well-known formulas (prediction and resetting of the covariance matrix). If K_(η)=1, the prediction model is not trusted: resetting consists of initialising the incorporation with {circumflex over (Q)}_(i) ^(EM)(t_(n)). If K_(n)=0, the measures are not trusted which are not taken into account. Adjustment of the gain does not form part of the invention, in particular because it depends a great deal on experimental conditions (noise, quality of the sensors, etc.).

The compensation of the latency is performed in the following manner: After the resetting of the filter according to [41] at the instant t_(n) ⁺the equations [35] to [38] are incorporated over a time t_(kg)−T_(obs)/2 up to t_(kg) (the current time), by using the raw angular velocities stored in memory over said time interval, and corrected according to [33-d]. The initial value of Q is the value reset at A new value of t_(n) ⁺. A new value of {dot over (Q)}(t_(kg)) is obtained. Then, from t_(kg) to

${t_{kg} + \frac{T_{obs}}{2}},$

at each new acquisition of {right arrow over (ω)}_(m), {dot over (Q)}(t_(kg)) is computed according to the same formulas [35] to [38] up to the new resetting value Q(t_(n+1)) date of the arrival of the new orientation of the tracker system (first orientation). Thus, the compensation has been carried out.

The direction cosine matrix R_(g/i)(t_(kg)) is computed defining the attitude of the gyrometers in the fixed mark and computed from the quaternion {dot over (Q)}(t_(kg))=[q₀ q₁ q₂ q₃]^(t) of [33] using the following formula:

$\begin{matrix} {R_{g/i} = \begin{bmatrix} {q_{0}^{2} + q_{1}^{2} - q_{3}^{2} - q_{4}^{2}} & {2\left( {{q_{1}^{2}q_{2}^{2}} - {q_{0}^{2}q_{3}^{2}}} \right)} & {2\left( {{q_{1}^{2}q_{3}^{2}} + {q_{0}^{2}q_{2}^{2}}} \right)} \\ {2\left( {{q_{1}^{2}q_{2}^{2}} + {q_{0}^{2}q_{3}^{2}}} \right)} & {q_{0}^{2} + q_{2}^{2} - q_{3}^{2} - q_{1}^{2}} & {2\left( {{q_{3}^{2}q_{2}^{2}} + {q_{0}^{2}q_{1}^{2}}} \right)} \\ {2\left( {{q_{1}^{2}q_{3}^{2}} - {q_{0}^{2}q_{2}^{2}}} \right)} & {2\left( {{q_{3}^{2}q_{2}^{2}} + {q_{0}^{2}q_{1}^{2}}} \right)} & {q_{0}^{2} + q_{3}^{2} - q_{1}^{2} - q_{2}^{2}} \end{bmatrix}} & \lbrack 42\rbrack \end{matrix}$

The matrix defining the direction cosines of the mark of the mobile object M relative to the reference mark (mark of the platform R_(P)) is then computed using the expression

R _(m/p)(t _(kg))=R _(p/i) ^(t)(t _(kg))R _(g/i)(t _(kg))R _(g/m) ^(t)  [43]

The second orientation may be defined by the Euler angles extracted from the matrix R_(m/p)(t_(kg)) using formulas known by the person skilled in the art.

said method makes it possible, on one hand, to provide at very high speed (in the order of 10 times faster) the estimation of the second orientation, which minimises the delay between the provision of the information computed and the use thereof by the system which carries out the acquisition thereof at any periodicity and in a manner not synchronised with t_(n), and on the other hand, the compensation of the latency by the computation of the trajectory of (t_(kg)−Tobs/2) at t_(kg) thanks to the storing in memory and correction of the gyrometric speeds of (t_(kg)−Tobs/2) at t_(kg).

Applications

The applications of the invention are mainly those for which significant accuracy is necessary for the position and orientation of a body relative to another body taken for reference in the presence of strong electromagnetic disturbances. The position and orientation of the helmet of civilian and military aircraft pilots without using magnetic maps is a first application. Numerous applications in surgery, in simulators, capture of movements and video games, etc., are possible.

FIG. 1

FIG. 1a : Prior art

FIG. 1b : Prior art

FIG. 1c : Prior art

FIG. 2: Object Marks Definition

Repère inertiel fixe R_(i) Fixed inertial frame R_(i) Objet P Object P Repère émetteur R_(E) fixé dans P Transmitting mark R_(E) attached to P Repère lié à M: R_(C1) Mark connected to M: R_(C1) Bloc C1 Block C1 Objet Mobile M Mobile object M Repère de R_(M) de M Mark R_(M) of M Repère R_(g) (gyromètres) Mark R_(g) (gyrometers) Repère R_(B) de C2 Mark R_(B) of C2 Bloc C2 Block C2 C3-2 lié à M C3-2 connected to M Repère R_(P) de P Mark R_(P) of P

FIG. 3: Overall Architecture of the Tracker System

OBJET P OBJECT P Bloc 4/E/C-2/C-3-2 Block 4/E/C-2/C-3-2 EMETTEUR TRANSMITTER CAPTEUR SENSOR Capteurs Inertiels Inertial Sensors Attitude P Attitude P PROCESSEUR PROCESSOR Capteurs vitesse angulaire de M M angular velocity sensors Sortie: Position orientation Output: Hybrid orientation hybridée position

FIG. 3′

FIG. 4: ARCHITECTURE OF THE TRACKER SYSTEM

Amplificateur Amplifier Réseau correcteur Corrector network Interface électrique Electrical interface Intégration Incorporation SBPA PRBS Processeur Embarqué On-board processor Acquisitions digitales Digital acquisitions Synchronisation Synchronisation Liaisons digitales Digital links ADC—Conversions ADC—Analogue/Digital Analogique/digitale Conversions CALCULS COMPUTATIONS SORTIE OUTPUT Générateur Séquence DCA or SBPA PRBS or ADC Sequence Generator Mesures inertielles Inertial measurements Mesure Attitude de P P Attitude Measurement Mesure Vitesses angulaires Object M angular velocity objet M measurement Capteur bruit Noise sensor

FIG. 5: control of emitted inductions

Consigne Setpoint Perturbations EMI EMI disturbances Harmoniques: B_(harmo) Harmonics: B_(harmo) Induction émise Emitted induction Réseau correcteur Corrector network Amplificateur de courant Current amplifier Bobinage Winding Noyau magnétique Magnetic core Interface électrique et Electrical interface and Intégration Incorporation Capteur_E Sensor_E

FIG. 6: transmitting block of prior art

3 Bobinages selon trois axes 3 Windings according to three non parallèles non-parallel axes Bloc de ferrite (Carré ou Ferrite block (Square or sphérique) spherical) Section Section

FIG. 7: formation of an axis E1 of the transmitter

FIG. 7-1 . . . FIG. 7-1, etc. Barreau isolé de Matériau Isolated bar of ferromagnetic ferromagnétique material Assemblage de Barreaux de Assembly of Bars of Matériaux ferromagnétique ferromagnetic material Section Section

FIG. 8: Examples of embodiment of transmission axes

FIG. 8-a: émetteur trois FIG. 8-a: non-concentric axes non concentriques three-axis transmitter Barreaux assemblés selon la Bars assembled according to FIG. 7 FIG. 7 Bobinages Windings FIG. 8-b: émetteurs trois FIG. 8-b: concentric three- axes concentriques axis transmitters

FIG. 9: Transmitter with core: Block consisting of interlocked sub-blocks

Bobinages 3 axes 3-axis windings Vue de face selon B-B Front view according to B-B Vue de face selon A-A Front view according to A-A

FIG. 10: control of the continuous field at zero

Détection crête Peak detection

FIG. 11: temporal transmission diagrams

EMISSION TRANSMISSION PAS D'EMISSION NO TRANSMISSION Sortie Output

FIG. 12-a: Hybrid tracker prior art

Détection crête Peak detection

FIG. 12-b: inertial extrapolator according to the invention

Attitudes plateformes (IRS) Platform attitudes (IRS) Capteurs inertiels Objet (IMU) Object inertial sensors (IMU) Calcul matrice de changements Mark change matrix computation de repère Intégration quaternions Incorporation of quaternions Estimation paramètres des Estimation of parameters of gyromètres gyrometers Compensation latence Latency compensation Détection de Position Magnetic tracking Magnétique Modèle de propagation des Model for propagation of erreurs gyromètres gyrometer errors 

1.-11. (canceled)
 12. A system for contactless determination of the position and orientation of a first mobile object (M) relative to a reference mark (R_(P)) carried by a second fixed or mobile object (P), in a disturbed electromagnetic environment, comprising: at least one electromagnetic sensor and at least one inertial sensor connected to the mobile object; at least one transmitter comprising at least one transmitting antenna, at least one inertial unit including inertial sensors connected to the platform; a computer for determining the orientation and position of the mobile object depending on the signals provided by the sensors and inertial sensors; and at least one reference electromagnetic sensor connected to the platform, the at least one transmitter comprising an incorporated electromagnetic sensor, the antenna of the at least one transmitter comprising ferromagnetic cores having effective relative magnetic permeability higher than 10, incorporating sensors for measuring the magnetic field X_(u) actually emitted by the axes of the transmitting sub-assembly that provide the variables for measuring the actual field emitted by the transmitter.
 13. The system according to claim 12, wherein the system comprises: a first assembly for transmitting magnetic induction(s), comprising a transmitting antenna and a first sub-assembly for transmitting Ne transmitting coils, Ne being equal to at least 2, the axes of symmetry of which, the sub-assemblies not being parallel to one another, being attached to the second object to form a reference mark; a first receiving assembly attached to the mobile object comprising Nc>=2 non-parallel receiving coils, sensitive to the ambient magnetic field resulting from the vector sum of the fields emitted by the first transmitting assembly and disturbing magnetic fields generated by electric currents existing in the environment and by ferromagnetic magnetizations, the second assembly forming a sensor secured to the first mobile object such that the product Nc*Ne>=6, and forming a measurement mark; a computing processor for computing the position and orientation of the first mobile object, coupled to a first analog/digital conversion means for carrying out the acquisition of analog signals at discrete times t_(k)=k·T_(e), second digital/analog conversion means for generating the predetermined currents injected into the first transmitting assembly; the antenna of the transmitting sub-assembly comprising ferromagnetic cores having effective relative magnetic permeability higher than 10, incorporating sensors for measuring the magnetic field X_(u) actually emitted by the axes of the transmitting sub-assembly that provide the variables X_(u)(j, t_(k)−k(i_(c))T_(e)) for j=1 to Ne and i_(c)=1 to Nc, means for extracting the signal correlated with the surrounding noise X_(BR)(t_(k)−k_(b)T_(e)) from the sensors rigidly connected to the platform in order to form with the magnetic induction measurement X_(u) a complete model of the measured fields making it possible to extract, without disturbers, while demultiplexing the channels emitted simultaneously, which makes it possible to compute the first position and orientation; means for hybridization comprising: i) at least one triaxial gyrometer rigidly connected to the mobile object and forming an inertial sub-assembly for IMU gyrometric measurements; ii) means for acquiring attitude information of an INS navigation unit connected to the platform; and iii) a system for detecting magnetic tracker posture connected to the mobile body and making it possible to cancel out the latency of the means for detecting position and for providing orientation information by computing the incorporation of a differential system governing the dynamics of the attitude of the object and that of sensor errors.
 14. The system according to claim 12, wherein the currents controlled by the computing processor are simultaneously emitted on the three axes continuously or discontinuously according to a cyclical temporal pattern of duration T_(obs)−T_(off)=N_(obs)·T_(e)−T_(off), the computing processor estimates, continuously and in real time with an output recurrence frequency F_(out) proportional to $\frac{1}{T_{obs}}$ equal or higher than the frequencies for refreshing video images, the parameters of an analytical model of the vector sum of all of the magnetic inductions present in the environment, the variables of the model being deduced: from the measurements taken by the third transmitting sub-assembly providing the j signals Xu_(j)(t_(k)) proportional to the emitted inductions, from the computation of variables of the type X_(cu)(j, t_(k)−k(i_(c))T_(e)) the linear combination of which is the model of the disturbances correlated with the transmission flux, and from the estimation of the signal sum of the disturbances radiated from the environment {circumflex over (B)}_(RM)(t_(k)) not correlated with the fields emitted by the coils of the transmitter, and either from the measurements of the second receiving block or extracted from the measurements of the signal from the first measurement block during the time T_(off) for switching off the transmission.
 15. The system according to claim 12, wherein the parameters A(i_(c),j) of the analytical model determined relative to the terms X_(U) _(j) (t_(k)) and to the measurement axis i_(c) of the first receiving assembly provide the terms of the dipolar or multipolar model of the inductive magnetic fields from the terms of which the computer determines a first value of the position and orientation of the sensor attached to the first mobile object on each transmission cycle T_(obs), the orientation defined by the three Euler angles Yaw Y, Pitch P, and Roll R.
 16. The system according to claim 12, wherein the Ne predetermined currents injected through Ne coils of a second transmitting assembly generate predetermined induction fluxes F_(j)(t) characteristic of each axis of the coils and cycles of period T_(obs), the value of which is close to periods for refreshing display screens, are such that the induction flux values continuously or discontinuously measured by the third transmitting sub-assembly and then digitized form temporal series that are not linearly dependent so as to form a reversible correlation matrix.
 17. The system according to claim 12, wherein the variables defining the portion of the model linearly dependent on Ne fluxes F_(j)(t) measured, j=1 to Ne, emitted by the Ne first transmitting sub-assemblies and received by the axis i_(c) of the first receiving assembly, comprises a linear combination of the type: ${B_{{CU}/E}\left( {i_{c},t_{k}} \right)}{\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{(i_{c})} = 0}^{N_{(i_{c})}}{{A_{CU}\left( {i_{c},j,k_{i_{c}}} \right)}{X_{CU}\left( {j,{t_{k} - {{k\left( i_{c} \right)}{Te}}}} \right)}}}}$ with ${\overset{\rightarrow}{X_{CU}}\left( {t_{k} - {k_{1}T_{e}}} \right)} = \left\lbrack {{X_{U\; 1}\left( {t_{k} - {k_{1}T_{e}}} \right)},{X_{U\; 2}\left( {t_{k} - {k_{1}T_{e}}} \right)},{X_{U\; 3}\left( {t_{k} - {k_{1}T_{e}}} \right)}} \right\rbrack^{t}$ in which the terms A_(C)(i_(c),j,k_(i)) for which k_(ic)=0 tend toward the values proportional to the inductive field that would be measured in free space in the absence of any magnetic disturbances, the other coefficients representing the values proportional to the inductions of the disturbing effects linearly dependent on the induction fluxes emitted.
 18. The system according to claim 12, wherein the model of the alternating signals of the environment of each component i_(c) of the first receiving assembly comprises a sum of signals of sinusoidal type ${B_{ESC}\left( {i_{c},t_{k}} \right)} = {{\sum\limits_{k_{sc} = 1}^{N_{sc}}{{\hat{C}}_{SC}^{re}{\left( {i_{c},k_{sc}} \right) \cdot {\cos \left( {\omega_{k_{sc}}{tk}} \right)}}}} + {{{\hat{C}}_{SC}^{im}\left( {i_{c},k_{sc}} \right)} \cdot {\sin \left( {\omega_{k_{sc}}{tk}} \right)}}}$ the frequencies ω_(k) _(sc) of which are estimated during the periods of non-emission T_(off) from the signals of the first receiving assembly to form the variables Xsc of a model grouping the sum of the model {circumflex over (B)}_(EC)(i_(c), t_(k)) and of the model B_(ESC)(i_(c), t_(k)): $B_{E} = {{\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{i_{c}} = 0}^{N_{i_{c}}}{{{\hat{A}}_{C}\left( {i_{c},j,k_{i_{c}}} \right)} \cdot {X_{C}\left( {i_{c},j,k_{i_{c}}} \right)}}}} + {\sum\limits_{k_{sc} = 1}^{N_{sc}}{{{\hat{C}}_{SC}^{re}\left( {i_{c},k_{sc}} \right)} \cdot {\cos \left( {\omega_{k_{sc}}t_{k}} \right)}}} + {{{\hat{C}}_{SC}^{im}\left( {i_{c},k_{sc}} \right)} \cdot {{\sin \left( {\omega_{k_{sc}}t_{k}} \right)}.}}}$
 19. The system according to claim 12, wherein the signal measured by the second receiving assembly B_(RM)(i_(c),t_(k)) is filtered to obtain the reference noise signal {circumflex over (B)}_(Ebr)(i_(c), t_(k)) by the following operations: B̂_(RM) = B_(C 2) − B̂_(CU)  with ${{\hat{B}}_{RU}\left( {i_{c},t_{k}} \right)} = {\sum\limits_{j = 1}^{N_{e}}\; {\sum\limits_{k_{b} = 0}^{N_{b}}{{A_{BRC}\left( {i_{c},j,k_{b}} \right)} \cdot {{X_{C}\left( {i_{c},j,k_{b}} \right)}.}}}}$
 20. The system according to claim 12, wherein the Nc coils of the first transmitting sub-assembly are wound around a cubic or spherical ferromagnetic core comprising cylinders or parallelepipeds, the length-to-diameter or length-to-width ratio of which is higher than 10 and the magnetic permeability is higher than 2000, the cylinders or parallelepipeds being interlocked in a substantially identical manner according to the three directions defined by the axes of symmetry of the windings and in such a way that the barycenter of the ferromagnetic matter of each axis is as close as possible to the common center of the three coils.
 21. The system according to claim 12, wherein currents injected by a second transmitting sub-assembly result from a large loop gain control of the direct chain, the setpoint of which is a cyclical signal generated digital/analogue conversion means in the processor, the cyclical signal being of constant spectral density (Pseudo-Random Binary Sequence) or dependent on the frequency, and the return signal subtracted from the setpoint being proportional to the induction from the third transmitting sub-assembly.
 22. The system according to claim 12, wherein the second orientation is computed in the following manner: at times t_(k)=k·T_(obs), the quaternion Q(t_(k)) defining the attitude of the gyrometers in the inertial frame (R_(i)) is computed from the terms of the matrices of direction cosines R _(g/i) ^(EM)(t _(k))={circumflex over (R)} _(p/i)(t _(k))·R _(m/p) ^(EM)(t _(k))·R _(g/m) the quaternion Q(t_(kg)=t_(k)+k_(g)·T_(g)) obtained by digital incorporation of the equation Q(t_(kg))= ${{Q\left( t_{k} \right)} + {\int_{t_{k}}^{t_{kg} = {t_{k} + {k_{g} \cdot T_{g}}}}{\frac{{A\left( {{\overset{\hat{\rightarrow}}{\omega}}_{m}(u)} \right)} \cdot {Q(u)}}{2}\ {u}}}},$  with Q(t_(k)) being taken from the resetting of the state vector X of the type X(t_(n) ⁺)=X(t_(n) ⁻)+K_(n)(Y−Ŷ) during reception of the orientation R_(m/p) ^(EM)(t_(k)) giving the measurement where ${A\left( {{\overset{\hat{\rightarrow}}{\omega}}_{m}(u)} \right)} = \begin{pmatrix} 0 & {- {{\hat{\omega}}_{mx}(u)}} & {- {{\hat{\omega}}_{my}(u)}} & {- {{\hat{\omega}}_{mz}(u)}} \\ {{\hat{\omega}}_{mx}(u)} & 0 & {+ {{\hat{\omega}}_{mz}(u)}} & {- {{\hat{\omega}}_{my}(u)}} \\ {{\hat{\omega}}_{my}(u)} & {- {{\hat{\omega}}_{mz}(u)}} & 0 & {{\hat{\omega}}_{mx}(u)} \\ {{\hat{\omega}}_{mz}(u)} & {{\hat{\omega}}_{my}(u)} & {- {{\hat{\omega}}_{mx}(u)}} & 0 \end{pmatrix}$ with {right arrow over ({circumflex over (ω)})}={right arrow over (ω)}_(m)−{right arrow over (δ{circumflex over (ω)})}, calculated from the values {right arrow over (ω)}_(m) provided by the gyrometers and corrected of errors of the gyrometers {right arrow over (δ{circumflex over (ω)})} estimated by an optimal estimator of the Kalman or sub-optimal type (“Least recursive squares” of the type LMS and RLS) according to a model for propagation of errors of the type {right arrow over (δ{circumflex over (ω)})}={right arrow over (ω)}_(b)+K·{right arrow over (ω)}_(m) where {right arrow over (ω)}_(b) is a random bias and K the matrix of gain, misalignment and coupling errors between channels; the direction cosine matrix R_(g/i)(t_(kg)) defining the attitude in the fixed mark is computed from the formula $R_{g/i} = \begin{pmatrix} {q_{0}^{2} + q_{1}^{2} - q_{3}^{2} - q_{4}^{2}} & {2\left( {{q_{1}^{2}q_{2}^{2}} - {q_{0}^{2}q_{3}^{2}}} \right)} & {2\left( {{q_{1}^{2}q_{3}^{2}} + {q_{0}^{2}q_{2}^{2}}} \right)} \\ {2\left( {{q_{1}^{2}q_{2}^{2}} + {q_{0}^{2}q_{3}^{2}}} \right)} & {q_{0}^{2} + q_{2}^{2} - q_{3}^{2} - q_{1}^{2}} & {2\left( {{q_{3}^{2}q_{2}^{2}} + {q_{0}^{2}q_{1}^{2}}} \right)} \\ {2\left( {{q_{1}^{2}q_{3}^{2}} - {q_{0}^{2}q_{2}^{2}}} \right)} & {2\left( {{q_{3}^{2}q_{2}^{2}} + {q_{0}^{2}q_{1}^{2}}} \right)} & {q_{0}^{2} + q_{3}^{2} - q_{1}^{2} - q_{2}^{2}} \end{pmatrix}$ where Q(t_(kg))=[q₀ q₁ q₂ q₃]^(t); the second orientation provided at t_(kg) is defined by the direction cosine matrix R_(m/p)(t_(kg)) defining the attitude of the mobile mark relative to the reference mark is then computed using the expression R _(m/p)(t _(kg))=R _(p/i) ^(t)(t _(kg)){circumflex over (R)} _(g/i)(t _(kg))R _(g/m) ^(t); and the second orientation being provided by the Euler angles extracted from the matrix R_(m/p)(t_(kg)).
 23. The system according to 13, wherein the mobile object comprises a helmet. 